# Dodecakis hecatonicosachoron

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Dodecakis hecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform dual |

Notation | |

Coxeter diagram | o5o3m3m () |

Elements | |

Cells | 1440 pentagonal pyramids |

Faces | 3600 isosceles triangles, 720 pentagons |

Edges | 1200+2400 |

Vertices | 120+600 |

Vertex figure | 120 dodecahedra, 600 triakis tetrahedra |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | Truncated hexacosichoron |

Abstract & topological properties | |

Flag count | 57600 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | Yes |

Nature | Tame |

The **dodecakis hecatonicosachoron**, also known as the **pentagonal-pyramidal chilliatetracositetracontachoron**, is a convex isochoric polychoron with 1440 pentagonal pyramids as cells. It can be constructed as the dual of the truncated hexacosichoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are times the length of those of the hecatonicosachoron. Varying the hexacosichoron's edge length to be anything less than times that of the hecatonicosachoron gives a fully symmetric variant of this polychoron.